The curability of selected cancers with certain chemotherapeutic drugs (notably alkylating agents) often has a direct relationship to dose in experimental systems, and admittedly with less data, in humans as well. Accordingly, increased doses should increase cure rates for these neoplasms. Autologous hematopoietic stem cell support (AHSCS) following intensive alkylating agent therapy allows substantial dose escalation in some cases; nonetheless, further escalation beyond these doses is usually limited by non-hematopoietic toxicity, so-called "regimen-related toxicity" (RRT). The chemoprotectant amifostine is the most promising agent currently available to limit RRT, having proven efficacious in preventing certain of these toxicities noted with alkylating agents, albeit when used in conventional dose. The primary aim of this study is to evaluate the efficacy of amifostine in preventing excessive RRT of the chemotherapy drug melphalan used in "transplant doses" of 220mg/m2 and greater. (In the main, we are concerned about mucosal toxicities, although other forms of RRT will be monitored.) If effective, amifostine may allow the safe use of even higher doses of melphalan than currently permitted, and these further- augmented doses may increase cures when melphalan is given in single or multiple courses, as sequential therapy or as components of intensive combinations. This concept will be tested in a standard Phase I-II study design in patients with myeloma (and perhaps other selected malignancies in the Phase I trial) who are not candidates for other transplant procedures. In addition, we will assay the pharmacokinetics of melphalan, as a prelude to eventually being able to give an individualized dose of melphalan to produce a standard area under the curve (AUC).